[Paper Review] Origin and fate of the pseudogap in the doped Hubbard model

Fedor Šimkovic, Riccardo Rossi+2 more|arXiv (Cornell University)|Sep 19, 2022

Physics of Superconductivity and Magnetism41 references20 citations

TL;DR

The paper uses controlled diagrammatic Monte Carlo to map the finite-temperature phase diagram of the doped 2D Hubbard model, identifying three regimes (weakly correlated metal, strongly correlated metal, and pseudogap) and connecting the pseudogap to spin fluctuations and eventual zero-temperature stripe order.

ABSTRACT

We investigate the doped two-dimensional Hubbard model at finite temperature using controlled diagrammatic Monte Carlo calculations allowing for the computation of spectral properties in the infinite-size limit and, crucially, with arbitrary momentum resolution. We show that three distinct regimes are found as a function of doping and interaction strength, corresponding to a weakly correlated metal with properties close to those of the non-interacting system, a correlated metal with strong interaction effects including a reshaping of the Fermi surface, and a pseudogap regime at low doping in which quasiparticle excitations are selectively destroyed near the antinodal regions of momentum space. We study the physical mechanism leading to the pseudogap and show that it forms both at weak coupling when the magnetic correlation length is large and at strong coupling when it is shorter. In both cases, we show that spin-fluctuation theory can be modified in order to account for the behavior of the non-local component of the self-energy. We discuss the fate of the pseudogap as temperature goes to zero and show that, remarkably, this regime extrapolates precisely to the ordered stripe phase found by ground-state methods. This handshake between finite temperature and ground-state results significantly advances the elaboration of a comprehensive picture of the physics of the doped Hubbard model.

Motivation & Objective

• Identify finite-temperature crossovers in the doped 2D Hubbard model as a function of doping and U.
• Characterize the weakly correlated metal, strongly correlated metal, and pseudogap regimes.
• Determine the magnetic correlation-length dependence of pseudogap formation.
• Explore whether spin-fluctuation theory can describe non-local self-energy components.
• Link finite-temperature pseudogap behavior to zero-temperature stripe ordering.

Proposed method

• Employ controlled diagrammatic Monte Carlo in the thermodynamic limit with arbitrary momentum resolution.
• Compute spectral properties via A(k) proxies and self-energies without analytic continuation.
• Decompose self-energy into local and non-local parts to analyze momentum dependence.
• Fit non-local self-energy to a spin-fluctuation-inspired ansatz with an Ornstein–Zernike form for chi_sp.
• Compare results to DMFT and DCA where appropriate.

Experimental results

Research questions

• RQ1 What are the finite-temperature crossovers between weakly correlated metal, strongly correlated metal, and pseudogap regimes in the doped 2D Hubbard model?
• RQ2 How do magnetic correlations and spin fluctuations drive the pseudogap, and how does this evolve with doping and U?
• RQ3 Can a modified spin-fluctuation theory capture the non-local self-energy in the pseudogap regime at both weak and strong coupling?
• RQ4 What is the fate of the pseudogap as T -> 0, and is it connected to ground-state stripe order?

Key findings

• Three regimes are identified: weakly correlated metal, strongly correlated metal, and pseudogap (PG) at low doping.
• The pseudogap originates from magnetic spin correlations and evolves with temperature and doping.
• A modified spin-fluctuation framework can describe the non-local self-energy in the PG regime at weak coupling and qualitatively at strong coupling.
• The pseudogap boundary extrapolates to the zero-temperature stripe-ordered ground state, indicating a 'handshake' with ground-state results.
• Lifshitz-type changes in Fermi surface topology accompany the PG, with a correlation-length dependence of spin fluctuations.
• Spectral weight suppression at antinodes and formation of Fermi arcs are observed in the PG regime.